I am no expert on file locking but I don't think that's possible.

It is.

$ touch lock

$ perl -M5.010 -MFcntl=LOCK_EX -e'
   open(my $fh, "<", "lock") or die $!;
   flock($fh, LOCK_EX) or die $!;
   say "ok";
'
ok
[download]

flock locks have nothing to do with reading and writing, and they prevent neither. They merely prevent locks from being obtained.